Question

5. 5y2 - 9x2 36

Answer 1

The given equation of the hyperbola is 5 y 2 −9 x 2 =36 .

5 y 2 −9 x 2 =36 (1)

The above equation can be written as,

y 2 ( 6 5 ) 2 − x 2 2 2 =1

Since the transverse axis is along the y axis, equation of the hyperbola can be represented as y 2 a 2 − x 2 b 2 =1 .(2)

Comparing equations (1) and (2), we get

a= 6 5 and b=2

c 2 = a 2 + b 2 c 2 = ( 6 5 ) 2 + 2 2 c 2 = 36 5 +4 c 2 = 56 5 c= 2 14 5

Since y axis is the transverse axis, coordinates of Foci = (0,±c)=( 0,± 2 14 5 )

Since y axis is the transverse axis, coordinates of Vertices = (0,±a)=( 0,± 6 5 )

Eccentricity = e = c a = 2 14 5 6 5 = 14 3

Length of Latus rectum = 2 b 2 a = 2 (2) 2 6 5 = 8 5 6 = 4 5 3

Thus, the coordinates of foci of hyperbola 5 y 2 −9 x 2 =36 are ( 0, ±2 14 5 ) , coordinates of vertices are ( 0,± 6 5 ) , eccentricity is 14 3 and length of latus rectum is 4 5 3 .